Consider following statements

$[1]$ $CM$ of a uniform semicircular disc of radius $R = 2R/\pi$ from the centre

$[2]$ $CM$ of a uniform semicircular ring of radius $R = 4R/3 \pi$ from the centre

$[3]$ $CM$ of a solid hemisphere of radius $R = 4R/3 \pi$ from the centre

$[4]$ $CM$ of a hemisphere shell of radius $R = R/2$ from the centre Which statements are correct?

$Assertion$ : The position of centre of mass of a body depends upon shape and size of the body.
$Reason$ : Centre of mass of a body lies always at the centre of the body.

The identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is_____

Define the position vector of centre of mass.

Infinite rods of uniform mass density and length $L, L/2, L/4....$ are placed one upon another upto infinite as shown in figure. Find the $x-$ coordinate of centre of mass

Two particles of mass $5\, kg$ and $10\, kg$ respectively are attached to the two ends of a rigid rod of length $1\, m$ with negligible mass. The centre of mass of the system from the $5\, kg$ particle is nearly at a distance of $..........\, cm$